展开 ((x^{11}+3)^{11})/(x^{99)}

解答

展开

\frac{( x ^{11} + 3 ) ^{11}}{x ^{99}}

x^{22} + 33 x^{11} + 495 + \frac{4455}{x ^{11}} + \frac{26730}{x ^{22}} + \frac{112266}{x ^{33}} + \frac{336798}{x ^{44}} + \frac{721710}{x ^{55}} + \frac{1082565}{x ^{66}} + \frac{1082565}{x ^{77}} + \frac{649539}{x ^{88}} + \frac{177147}{x ^{99}}

求解步骤

\frac{( x ^{11} + 3 ) ^{11}}{x ^{99}}

(x^{11} + 3)^{11} = x^{121} + 33 x^{110} + 495 x^{99} + 4455 x^{88} + 26730 x^{77} + 112266 x^{66} + 336798 x^{55} + 721710 x^{44} + 1082565 x^{33} + 1082565 x^{22} + 649539 x^{11} + 177147

= \frac{x ^{121} + 33 x ^{110} + 495 x ^{99} + 4455 x ^{88} + 26730 x ^{77} + 112266 x ^{66} + 336798 x ^{55} + 721710 x ^{44} + 1082565 x ^{33} + 1082565 x ^{22} + 649539 x ^{11} + 177147}{x ^{99}}

使用分式法则:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{x ^{121} + 33 x ^{110} + 495 x ^{99} + 4455 x ^{88} + 26730 x ^{77} + 112266 x ^{66} + 336798 x ^{55} + 721710 x ^{44} + 1082565 x ^{33} + 1082565 x ^{22} + 649539 x ^{11} + 177147}{x ^{99}} = \frac{x ^{121}}{x ^{99}} + \frac{33 x ^{110}}{x ^{99}} + \frac{495 x ^{99}}{x ^{99}} + \frac{4455 x ^{88}}{x ^{99}} + \frac{26730 x ^{77}}{x ^{99}} + \frac{112266 x ^{66}}{x ^{99}} + \frac{336798 x ^{55}}{x ^{99}} + \frac{721710 x ^{44}}{x ^{99}} + \frac{1082565 x ^{33}}{x ^{99}} + \frac{1082565 x ^{22}}{x ^{99}} + \frac{649539 x ^{11}}{x ^{99}} + \frac{177147}{x ^{99}}

= \frac{x ^{121}}{x ^{99}} + \frac{33 x ^{110}}{x ^{99}} + \frac{495 x ^{99}}{x ^{99}} + \frac{4455 x ^{88}}{x ^{99}} + \frac{26730 x ^{77}}{x ^{99}} + \frac{112266 x ^{66}}{x ^{99}} + \frac{336798 x ^{55}}{x ^{99}} + \frac{721710 x ^{44}}{x ^{99}} + \frac{1082565 x ^{33}}{x ^{99}} + \frac{1082565 x ^{22}}{x ^{99}} + \frac{649539 x ^{11}}{x ^{99}} + \frac{177147}{x ^{99}}

\frac{x ^{121}}{x ^{99}} = x^{22}

\frac{33 x ^{110}}{x ^{99}} = 33 x^{11}

\frac{495 x ^{99}}{x ^{99}} = 495

\frac{4455 x ^{88}}{x ^{99}} = \frac{4455}{x ^{11}}

\frac{26730 x ^{77}}{x ^{99}} = \frac{26730}{x ^{22}}

\frac{112266 x ^{66}}{x ^{99}} = \frac{112266}{x ^{33}}

\frac{336798 x ^{55}}{x ^{99}} = \frac{336798}{x ^{44}}

\frac{721710 x ^{44}}{x ^{99}} = \frac{721710}{x ^{55}}

\frac{1082565 x ^{33}}{x ^{99}} = \frac{1082565}{x ^{66}}

\frac{1082565 x ^{22}}{x ^{99}} = \frac{1082565}{x ^{77}}

\frac{649539 x ^{11}}{x ^{99}} = \frac{649539}{x ^{88}}

= x^{22} + 33 x^{11} + 495 + \frac{4455}{x ^{11}} + \frac{26730}{x ^{22}} + \frac{112266}{x ^{33}} + \frac{336798}{x ^{44}} + \frac{721710}{x ^{55}} + \frac{1082565}{x ^{66}} + \frac{1082565}{x ^{77}} + \frac{649539}{x ^{88}} + \frac{177147}{x ^{99}}

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